Which mathematical transform is used to reconstruct raw MRI data into images?

• A. Laplace transform
• B. Inverse transform
• C. Wavelet transform
• D. Fourier transform

Answer: (D)

In MRI, the raw data are collected in k-space, which is the spatial-frequency representation of the image. To form the image, you convert that frequency-domain data back into the spatial domain by applying the inverse Fourier transform. In practice this is done as a 2D inverse FFT to reconstruct the image from the acquired k-space samples. The Fourier relationship is fundamental here because k-space encodes how different spatial frequencies contribute to the final image; summing those frequencies with the right phases yields the actual image. While the process is often described in terms of the Fourier transform, the key operation is the inverse Fourier transform converting frequency data into spatial intensities.